Magnetic Field Effects in Triplet-Triplet Annihilation Upconversion: Revisiting Atkins and Evans' Theory

In their seminal description of magnetic field effects on chemiluminescent fluid solutions, Atkins and Evans considered the spin-dependent interactions between two triplets, incorporating the effects of the diffusion of the molecules in the liquid phase. Their results, crucial for the advancement of photochemical upconversion, have received renewed attention due to the increasing interest in triplet-triplet annihilation for photovoltaic and optoelectronic applications. Here we revisit their approach, using a modern formulation of open quantum system dynamics and extend their results. We provide corrections to the theory of the magnetic field response of the fluorescent triplet pair state with singlet multiplicity. These corrections are timely, as improvements in the precision and range of available experimental methods are supported by the determination of quantitatively accurate rotational and interaction model parameters. We then extend Atkins and Evans' theory to obtain the magnetic field response of triplet pair states with triplet and quintet multiplicity. Although these states are not optically active, transitions between them are becoming imperative to study the working mechanism of spin-mediated upconversion and downconversion processes, thanks to advances in electron spin resonance and time-resolved transient absorption spectroscopy.